Solutes unmask differences in clustering versus phase separation of FET proteins

Phase separation and percolation contribute to phase transitions of multivalent macromolecules. Contributions of percolation are evident through the viscoelasticity of condensates and through the formation of heterogeneous distributions of nano- and mesoscale pre-percolation clusters in sub-saturated solutions. Here, we show that clusters formed in sub-saturated solutions of FET (FUS-EWSR1-TAF15) proteins are affected differently by glutamate versus chloride. These differences on the nanoscale, gleaned using a suite of methods deployed across a wide range of protein concentrations, are prevalent and can be unmasked even though the driving forces for phase separation remain unchanged in glutamate versus chloride. Strikingly, differences in anion-mediated interactions that drive clustering saturate on the micron-scale. Beyond this length scale the system separates into coexisting phases. Overall, we find that sequence-encoded interactions, mediated by solution components, make synergistic and distinct contributions to the formation of pre-percolation clusters in sub-saturated solutions, and to the driving forces for phase separation.

1.A difficulty with reading the article comes from the fact that the authors do not provide a clear description of the expected quantitative, experimentally observable differences between phase separation and percolation processes.What does one expect if the observed clusters (meso-or macro-) are formed by separation or percolation?Does one expect a difference in cluster size distribution for the same concentration point?Intuitively, phase separation vs. percolation should be behave quite differently since in the first case it is an all-or-nothing transition (no clusters observed until threshold concentration) and in the latter case a continuum of clusters should appear at concentrations below the percolation threshold.
2. The experimental methods used in the study rely mostly on monitoring particle diffusion (e.g.DLS, FCS, NTA) and, as such, they report on the apparent sizes, but not the masses of cluster i.e. the number of proteins in them.It is important that the effects are clearly demonstrated for the mass distribution of clusters.For example, can the derived count rates in DLS data be converted to SLS intensities and be related to mass (Figure 2 g-i, Figure S3 g-h)?This is important as the observed changes in the apparent hydrodynamic size can have many different explanations, e.g. protein can become swollen in one buffer and compact in another and the same could translate to their respective oligomers.In other words, two clusters can contain the same number of proteins, while being of a different hydrodynamic diameter.Conversely, they can have the same diameter, while containing a very different number of proteins.
2. In light of this, the authors should directly assess the conformational properties of single protein molecules in different environments.
3. Importantly, in the absence of a precise estimation of the size of the clusters in terms of mass or number of proteins, any thermodynamic arguments or estimates related to the free energy of transfer of FUS molecules from the dispersed phase into mesoscale clusters in glutamate versus chloride cannot be made.For example, on L172-173, the authors estimate that this difference is 0.5-0.75kcal/mol, but this must come from a tacit assumption that the abundance of mesoscale clusters is a direct measure of the amount of protein molecules contained in them, which need not be the case.As already mentioned, the authors should measure the sizes of clusters in terms of the mass of proteins they contain or, at least, clearly state and critically discuss the assumptions behind connecting cluster sizes with protein mass.In general, the authors should from the start precisely define what they mean by "size of clusters" throughout.This is not just a semantic point, but rather concerns the very essence of the arguments made.4. Record and coworkers (PMID: 27806267, 27054379) have provided a quantitative model of how Glu impacts protein stability in relation to the amount and composition of surface area exposed or buried.While the authors cite these studies, they contain much more relevant information than presently exploited by the authors.In particular, the authors should study the predictions of the model by Record et al. in the case of FUS sequence and critically analyze what they imply about their findings.5. What is the contribution of protein net charge to the observed effects?E.g. Figure 2. g-i the net charges of the constructs are 10, -1, 12, respectively.As Glu is both a pi system and an anion, are there any implications concerning the anion-pi interactions?6.On p. 4, the authors claim that "In KGlu, the slow modes appear at protein concentrations of 2 μM (Supplementary Figure 2e), whereas in KCl they appear at 3 μM.These results provide independent confirmation of the estimates of csat and emphasize the small differences in driving forces for macrophase separation of FUS-SNAP in 100 mM KCl versus 100 mm KGlu".How significant is this difference?Also, there does not appear to be a strong difference between panels in Supplementary Figures 2a and g.Moreover, since the sample is polydisperse, were there any regularization fits used to obtain size distributions?Also, the effect on the autocorrelation curves looks more prominent in panel c and not so in f.Since DLS has a detection limit, (e.g.0.5 mg/ml or so), autocorrelation curves should also presented for low protein concentrations (below 1 µM).7. On p. 7, the authors claim that "the derived count rate for FUS-SNAP is up to 3-fold higher in 100 mM KGlu when compared to 100 mM KCl (Fig. 2g).Untagged FUS shows similar behaviors (Supplementary Figure 3g)."This is not immediately apparent, especially when it comes to quantitative differences.Also, the effect is not so prominent for another construct (FUS-EGFP).Finally, different constructs also have different net charges FUS WT 14, FUS-SNAP 10, FUS-EGFP 6.How does this impact the comparison?8.The claimed difference between Arg and Lys residues should be more precisely phrased and better explained in light of the existing literature on the topic (p. 8 "Indeed, it is noteworthy that the free energies of solvation of Arg and Lys are fundamentally different from one another.From this hydration perspective, Arg has more of a hydrophobic character than Lys.As a result, the driving forces for phase separation, which are governed mainly by solubility, are affected by the substitution of Arg to Lys significantly.") 9. On p. 6, the authors claim that "Further, measurements of fluorescence correlation spectroscopy (FCS) on the single-molecule level show that the autocorrelation of donor-labelled FUS-SNAP is consistent with increased translational diffusion time td2 and strong fluctuation in the weighted residuals at correlation times longer than td2 in the KGlu buffer (Supplementary Figure 3f).This points to the presence of higher-order complexes even at 400 pM concentrations of FUS-SNAP.".However, it is hard to see any difference.This should be shown quantitatively together with an estimation of how significant the effect is.Also, since here one again deals with polydisperse media, how appropriate is it to just use a two-component fit?
Extant data suggest that the sequence determinants of clustering in sub-saturated solutions and the solution-condition-specific values of csat can be both synergistic and distinct 42 .For example, several mutations with FET proteins were found to affect clustering and phase separation equivalently.However, separability of interactions was also demonstrated by the effects of solutes that dissolve condensates but do not influence clustering in sub-saturated solutions 42 .Likewise, while certain mutations impact clustering, they have a minimal impact on phase separation, especially if csat is already low.The recent study of Lan et al. reported findings for Negative Elongation Factor (NELF) that support the separation of interactions that determine sub-saturated solution clusters versus condensation in live cells 43 .These observations suggest that, in some systems, clustering and phase separation are likely to be governed by partially separable energy scales.Here, we investigated whether changing the solution anion from chloride to glutamate would have separable effects on the driving forces for phase separation versus clustering in sub-saturated solutions.
Our choice of comparing the effects of chloride versus glutamate on clustering versus phase separation was motivated by two considerations: First, glutamate tends to drive protein-protein associations 44,45 .This, we reasoned, should enhance clustering in sub-saturated solutions.Second, cellular milieus are complex mixtures of ions, metabolites, and osmolytes 46, 47 .The high concentrations of potassium (~150 mM) are balanced by anions that include the amino acid glutamate, glutathione, and organic phosphates 47,48 .Importantly, the relevant anion inside cells is glutamate and other organic phosphates whereas the intracellular concentrations of chloride are very low in comparison (see Supplementary Table S1 for information regarding glutamate) 46,47 .
Finally, we provide the following rationale, starting on line 140 of the revised manuscript.
We reasoned, based on our findings regarding the different effects of solutes on clustering versus phase separation of FET proteins 42 , that studying clustering in glutamate versus chloride would allow us to assess whether interactions that drive clustering / percolation are separable from those that drive phase separation.
In the revised discussion section, we summarize our results and provide comparative assessments with the work of Kozlov et al., that is also discussed extensively.Please see the following text, which starts on line 513 of the revised manuscript: In the mean-field formalism of Flory 32 and Huggins 33 , the solubility parameter c is proportional to the algebraic difference between the effective protein-solvent interactions and the arithmetic mean of protein-protein and protein-solvent interactions 5 .For associative macromolecules, Tanaka introduced the concept of a renormalized c to account for the effects of specific intermolecular associations, and the interplay with the solventspecific interactions 36 .The renormalized c depends on macromolecular concentrations and it combines the contributions of specific sticker-stickers interactions, their mediation by solvent, and the effects of the interplay between solubility-determining macromolecule-solvent interactions and solvent-solvent interactions.In glutamate, our data show that associations of FET proteins are strengthened on the nanoscale.However, these do not translate to significant changes in csat.The implication is that, for FET proteins, the renormalized c is similar in chloride versus glutamate.This suggests that the enhancement of protein-protein interactions on nanoscales is counterbalanced by length-scale-dependent changes to macromolecule-solvent interactions and / or weakened solvent-solvent interactions in glutamate versus chloride.This would explain why cluster formation in subsaturated solutions is enhanced, but csat changes only minimally.
Our findings regarding the relative insensitivity of csat to glutamate versus chloride differ from those of Kozlov et al. for bacterial SSBs 54 .This suggests that the interplay of solvent-mediated specific associations and solubility-determining interactions are not generic across different systems, but they are instead sequence-and architecture-specific.While FET proteins are flexible, linear associative polymers, the SSBs are protein-based exemplars of branched "hairy colloids" 70,71 .Taken together with the results of Kozlov et al., 54 our work highlights the need for comparing the effects of glutamate and other cellular metabolites on clustering and phase separation of multivalent proteins defined by different sequence grammars and architectures.
Our comparative assessments of chloride versus glutamate were motivated by the fact that the latter is an exemplar of the types of anions that are present in cells.Yet, it is often assumed that physiologically relevant salt conditions correspond to 100 -150 mM KCl or NaCl 72,73,74,75,76 .This assumption does not square with extant data for prokaryotic 47 or eukaryotic systems.For example, in the cytoplasms of glutamatergic neurons, the concentration of glutamate is in the 5 -10 mM range 77 .In synaptic vesicles, glutamate concentrations can be as high as 100 mM 78 .Formulations for a "single-assay medium" intended to mimic the in vivo medium of Saccharomyces cerevisiae lead to the following prescription: 300 mM K + , 245 mM glutamate, 50 mM phosphate, 20 mM Na + , 2 mM free Mg 2+ , all at a pH of 6.8 48 .Importantly, the mimicking medium does not include chloride.Therefore, RNA-binding proteins are unlikely to encounter chloride inside cells.Instead, glutamate or other metabolites including phosphates are likely to be the key anions, thus highlighting the biological relevance of findings reported in this work.
Comment 2: Introduction.Please give explanation to the fact that ATP and 1,6-hexanediol dissolve condensates while do not affect the clustering.
Response to comment 2: This topic was discussed extensively in Ref. 42, which is the original work of Kar et al., and we do not discuss it here.To avoid distractions, we have deleted mentions of ATP and 1,6-hexanediol, since these solutes are not the focus of the current work.

Comment 3: Page 9. The authors used two fluorescent probes, Nile red and bis-ANS. As Nile red shows increased quantum yields in nonpolar environments, what is the property of bis-ANS in response to its environment?
Response to comment 3: We have rewritten the relevant section and added supplementary figures to provide an explanation of this issue.The following text, which starts on line 425, alongside Fig. 6, address the issue raised by the reviewer.
Clusters create unique local environments: Next, we used environmentally-sensitive dyes, specifically Nile red and bis-ANS, to probe the physicochemical properties of clusters that form in different buffers.The quantum yields of both dyes show increased quantum yields in nonpolar environments 46,73,74 .We measured the fluorescence lifetime distributions of Nile red using MFD in various concentrations of FUS-SNAP in 100 mM KGlu and 100 mM KCl. Nile Red exhibits a spectrum of lifetimes ranging from 0.6 ns to 4.66 ns.It is known the lifetimes of Nile Red increase with increased hydrophobicity 75 .In 100 mM KCl, at 0.5 µM FUS-SNAP, the peak in the fluorescence lifetime distribution occurs at 2 ns.With increasing concentration of FUS-SNAP, the lifetime distribution in 100 mM KCl becomes bimodal, showing peaks at 2 ns and 4 ns.In the presence of 100 mM KGlu, the Nile Red lifetime distributions show one distinct peak with an average lifetime of 4 ns, which is reached at FUS-SNAP concentrations as low as 0.5 µM.The inference is that there is an increase in the number and size of clusters in KGlu compared to KCl (Fig. 7a).To complement the analysis with Nile Red, we also used bis-ANS to probe the local environments within clusters that form in the presence of 100 mM KGlu versus 100 mM KCl (Fig. 7b and 7c).In both cases, in the presence of 2 µM bis-ANS concentration, the fluorescence intensity increases with increasing protein concentration.The increase in intensity is higher in the presence of KGlu compared to KCl.As a control, when we increased the KCl concentration to 200 mM, it caused a decrease in the fluorescence intensity of bis-ANS with FUS-SNAP compared to 100 mM KCl buffer.This suggests that KCl inhibits the clustering of FUS-SNAP.To assess the hydrophobicity of the clusters, the fluorescence intensity of the same concentration of bis-ANS was measured in methanol and ethanol (Supplementary Fig. S7b).The intensity of bis-ANS in the presence of FUS-SNAP clusters in KGlu buffer is comparable to that of bis-ANS in methanol.These findings suggest that clustering in sub-saturated solutions is enhanced in KGlu when compared to KCl.Stronger molecular associations increase the extent of clustering, as probed via the sizes of clusters, and the larger clusters are internally more hydrophobic when compared to the surrounding solvent.

Summary comments: Kar and coworkers present a combined experimental/computational analysis of the impact of glutamate anions, major constituents of the cytosol, on the formation of biomolecular condensates of protein FUS and other members of the FET protein family. As the main theme of the study, they compare and contrast the impact of glutamate with that of chloride ions within a framework in which percolation is coupled with phase transition in condensate formation. The question of the mechanistic foundation of biomolecular condensate formation is an important one and the authors
provide several relevant and thought-provoking results in this regard.However, there is a number of key issues that need to be addressed adequately before the suitability of the manuscript for publication in Nature Communications can be assessed.

Response to summary comments:
We thank the reviewer for providing a detailed assessment of our work.Below, we provide a detailed point-by-point response and an inventory of the revisions we have made in response to the comments made the reviewer.
Comment 1: A difficulty with reading the article comes from the fact that the authors do not provide a clear description of the expected quantitative, experimentally observable differences between phase separation and percolation processes.What does one expect if the observed clusters (meso-or macro-) are formed by separation or percolation?Does one expect a difference in cluster size distribution for the same concentration point?Intuitively, phase separation vs. percolation should be behave quite differently since in the first case it is an all-or-nothing transition (no clusters observed until threshold concentration) and in the latter case a continuum of clusters should appear at concentrations below the percolation threshold.

Response to comment 1:
We have revised the introduction to provide a clear distinction of phase separation sans percolation versus phase separation coupled to percolation.The following revisions and inclusions are provided, starting on line 39 of the revised manuscript.Please note that this includes a new figure to answer the query as directly as possible.
In vitro, in the presence of 150 mM KCl and at a pH of ~7.2, FET proteins purified from insect cells will undergo phase separation above sequence-specific saturation concentrations (csat) 10 .The sequence-dependencies of measured csat values were rationalized using the framework of linear associative polymers 12 , which can be used to parse the sequences of FET proteins into stickers versus spacers 10,13,14,15,16,17 .Stickers engage in strong, specific interactions, and they form reversible physical crosslinks with one another.Spacers contribute to the cooperativity of sticker-sticker interactions 6,16,18 .They also contribute to macromolecular solubility through the balance of spacer-spacer, spacer-sticker, and spacer-solvent interactions 19,20,21 .Distinct hierarchies of interactions that enable the classification of residues or motifs as stickers versus spacers enables the mapping of different heteropolymeric systems onto linear associative polymers.These include the intrinsically disordered RGG domains of DDX4 and LAF-1 22, 23, 24 , full-length FET proteins 10 , their RBDs and PLCDs 19, 20, 21, 25, 26 , the condensate driving domains of chromatin remodeling complexes 27 , the stress granule protein UBQLN2 28 , and unfolded states of intrinsically foldable domains 17 .
Phase transitions of associative macromolecules combine phase separation and percolation 5,29 .The latter is also known as thermoreversible gelation 12,13,30,31 .The solubility limits of macromolecules, influenced by solvent-mediated intermolecular interactions, will lead to the separation of a macromolecular solution into coexisting dense and dilute phases 32,33 .Equalization of chemical potentials and osmotic pressure 34 will determine macromolecular concentrations in dense and dilute phases, and we designate these as cden and cdil, respectively.Note that cdil equals csat.Phase separation is a segregative transition because the macromolecular solution separates into coexisting dense and dilute phases to minimize the overall free energy of mixing of macromolecular and solvent components 5,35 .
Multivalence, defined by the numbers of stickers of different types, will enable the networking of associative macromolecules through the formation of clusters that grow continuously with increasing numbers of molecules being incorporated into networks as concentrations increase 5,13,16,36 .These continuous transitions are defined by a percolation threshold (cperc) above which a system-spanning network forms 5,31,36,37,38 .As clusters grow, they will influence solubility.This is because, as emphasized by Ogston 39 , overall solubility is governed by a combination of the sizes and physicochemical properties of clusters that form via intermolecular associations 36 .For associative macromolecules that undergo phase separation it follows that csat < cperc < cden 5,6,13,14 .As a result, associative macromolecules that undergo phase separation will also undergo percolation, with the dense phase being a physically crosslinked network that spans the condensate 5,21,40 .This gives condensates an underlying network-like sub-structure that generates sequence-specific viscoelastic moduli 41 .Gelation or percolation sans phase separation will occur if cperc < csat 6 .
A direct upshot of the coupling of phase separation and percolation is the presence of pre-percolation clusters in sub-saturated solutions 36 .Theory predicts that the average cluster size will grow continuously with concentration, where sizes are defined by the numbers of molecules within clusters (Fig. 1) 5,36 .In accord with these expectations, recent studies, which deployed a diverse suite of measurements spanning a wide range of concentrations, showed that FET family proteins form heterogeneous distributions of pre-percolation clusters in sub-saturated solutions 42 .With increasing protein concentration, the clusters in sub-saturated solutions grow continuously in size and abundance.The distributions of cluster sizes in sub-saturated solutions are heavy-tailed 5, 42 (Fig. 1).This affords a finite likelihood of forming mesoscale species, hundreds of nanometers in diameter.The presence of these species contributes to saturating the soluble phase, thus contributing to the determination of csat.Indeed, as shown previously 42 , systems with weak clustering are also characterized by larger csat values.Above csat, condensate formation of FET proteins is driven by the separation of large and small species via clustercluster coalescence and the networking of mesoscopic clusters that form in sub-saturated solutions 42 .Fig. 1: Cluster size distributions in sub-saturated solutions for different processes.If phase separation does not involve associative interactions and is driven by a single energy scale, viz., macromolecular solubility, then the cluster size distribution will be bounded, as shown by the dashed line.However, if specific interactions between stickers contribute to associations, then the cluster size distribution evolves continuously, showing a rightward shift as csat is approached -see solid lines.The ordinate quantifies P(n), the probability density associated with a cluster comprising n molecules, which is the label along the abscissa.
Extant data suggest that the sequence determinants of clustering in sub-saturated solutions and the solution-condition-specific values of csat can be both synergistic and distinct 42 .For example, several mutations with FET proteins were found to affect clustering and phase separation equivalently.However, separability of interactions was also demonstrated by the effects of solutes that dissolve condensates but do not influence clustering in sub-saturated solutions 42 .Likewise, while certain mutations impact clustering, they have a minimal impact on phase separation, especially if csat is already low.The recent study of Lan et al. reported findings for Negative Elongation Factor (NELF) that support the separation of interactions that determine sub-saturated solution clusters versus condensation in live cells 43 .These observations suggest that, in some systems, clustering and phase separation are likely to be governed by partially separable energy scales.Here, we investigated whether changing the solution anion from chloride to glutamate would have separable effects on the driving forces for phase separation versus clustering in sub-saturated solutions.

Comment 2:
The experimental methods used in the study rely mostly on monitoring particle diffusion (e.g.DLS, FCS, NTA) and, as such, they report on the apparent sizes, but not the masses of cluster i.e. the number of proteins in them.It is important that the effects are clearly demonstrated for the mass distribution of clusters.For example, can the derived count rates in DLS data be converted to SLS intensities and be related to mass (Figure 2 g-i, Figure S3 g-h)?This is important as the observed changes in the apparent hydrodynamic size can have many different explanations, e.g. protein can become swollen in one buffer and compact in another and the same could translate to their respective oligomers.In other words, two clusters can contain the same number of proteins, while being of a different hydrodynamic diameter.Conversely, they can have the same diameter, while containing a very different number of proteins.

Response to comment 2:
As explained in response to comment 3 (please see below), we have added new, single molecule measurements to test whether there are conformational changes that occur and are different between the two buffers.We do not find any evidence for the proposed conformational changes.Furthermore, such conformational changes would have to be quite significant for them to manifest as differences in hydrodynamic sizes in scattering measurements.Even more importantly, we draw the reviewer's attention to the fact that the single molecule measurements -both the original data and the new data -which provide assessments regarding the numbers and brightness per molecule, irrespective of conformational changes, while also investigating the prospect of conformational changes, provide a clear denouement in favor of clustering rather than changes to scattering based purely on conformational changes.Indeed, the sizes of scatterers we observe in the NTA measurements would not be realizable based purely on conformational transitions in the single molecule regime.As for the request to convert the DLS data to SLS intensities, this can only be done if we had access to multi-angle DLS data.Here, the DLS data were collected at 173˚.Likewise, for mass measurements, we would need a combination of static right-angle light scattering and lowangle light scattering or multi-angle light scattering.Even these methods, which will always be heavily influenced by Rayleigh scattering, will not be effective for deconvolution of mass distributions because our samples, as unequivocally shown by the single-molecule and multiparameter fluorescence data, have significant heterogeneities.
Comment 2: In light of this, the authors should directly assess the conformational properties of single protein molecules in different environments.

Response to comment 2:
We have added a new section and a brand new, multi-panel figure (Fig. 4) that directly addresses this point.The relevant inclusions may be found starting on line 282 and are reproduced here for the benefit of the reviewer.Importantly, we have used sensitive measurements of conformation at ultra-low proteins concentrations and quantified the differences in cluster size distributions across a range of protein concentrations in the two buffers.We do not find any evidence of conformational differences between the two buffers.

FCS and NanoDSF also show enhanced stabilization of FUS clusters in glutamate:
IUPRED analysis 60 predicts that isolated FUS mainly consists of disordered regions (Fig. 4a).However, given extant sequenceensemble characterizations of disordered proteins, it stands to reason that there will be conformational fluctuations that are differently impacted by glutamate versus chloride.To investigate the influence of both buffers on the stabilization of FUS in monomers and in clusters, we studied FUS-SNAP-AF488 in a complementary approach by FCS at the single-molecule level and by nanoscale differential scanning fluorimetry (nanoDSF) at concentrations close to saturation where the signals will be dominated by larger, non-monomeric species.
We studied single-molecule events in equilibrated solutions with FUS-SNAP-AF488 in KGlu and KCl, respectively (Fig. 4b).Comparing both signal traces, it is evident, that the bursts in KGlu are brighter and more frequent.We computed the autocorrelation functions of FUS-SNAP-AF488 for two intensity-based selections: monomers and clusters.For the preferential selection of monomers, all bright bursts above its intensity threshold are excluded.In Fig 4c, we show correlation curves for FUS monomers together with the free dye measurement of rhodamine 110 as reference.The data for FUS were fit using a model (see Methods, eq.6a) with two components for translational diffusion: one global time for dye impurities and one salt-dependent time for monomeric FUS.In the panels on the right, we show two blow-ups of the correlation curves centered at the respective diffusion times of FUS monomers, td,monomer, (dark yellow) and clusters, td,cluster (pink).For FUS monomers, the correlation curves in KCl and KGlu overlap, and the fitted diffusion times are identical within error.Using the Stokes-Einstein equation, we converted these times to an average hydrodynamic radius of 2.3 nm.The distinct buffers do not change the overall size of monomeric FUS.
In contrast to the monomer sub-population, the long diffusion time td,cluster (Fig. 4d) of FUS clusters in KGlu differs from the value in KCl by ~ 1 ms (Supplementary Table S4).Furthermore, large deviations in the weighted residuals indicate the insufficiency of a two-component fit for FUS clusters in glutamate.Thus, we applied the Maximum Entropy Method (MEM) as a model free approach 61, 62 to quantify the diffusion time distributions for clusters (Fig. 4e).Two peaks were obtained for both buffers.To verify the goodness of the fit and demonstrate appropriate weighting, we display the dependence of the reduced χ 2 red on the entropy (L-curve, Fig. 4f), where the chosen values of the corner point are marked with a dot (see Methods and Supplementary Fig. S6).Due to the larger fraction of clusters, a higher minimum χ 2 red is yielded for KGlu.The first peak at td,monomer ~ 0.2 ms resembles the monomer species and they overlap for KCl and KGlu.The second peak, which is in the millisecond time range, corresponds to clusters.In KGlu, the peak has significantly longer times and higher amplitudes than in KCl.From this we conclude that FUS clusters are more abundant and larger in size in KGlu, even though there are no detectable conformational differences at the level of FUS monomers.Instead, glutamate enhances macromolecular associations when compared to chloride, and this is in line with the previous reports 50, 55 .
Glutamate is known to enhance protein stability 45 .Although FUS is intrinsically disordered, its overall dimensions and the heterogeneity of intramolecular interactions, quantified via accessibility of different functional groups, will be temperature dependent.Accordingly, we investigated how buffers influence the temperature dependence of tryptophan fluorescence of FUS-SNAP.For this, we performed nanoDSF measurements, which helps us analyze the consequences of thermal fluctuations in low-volume capillaries.Increasing the temperature will drive increased exposure of tryptophan residues.NanoDSF monitors the concurrent changes in tryptophan fluorescence at 330 and 350 nm 63 .To increase the measurement sensitivity, we used FUS-SNAP instead of FUS.This helps minimize the amount of residual KCl caused by the storage buffer, and it enables improved signal strength.
Fig. 4g shows changes of the 350 nm / 330 nm ratio as a function of increasing temperature in two different concentrations and buffers.The first derivative plot (Fig. 4h) shows that the apparent unfolding temperature of FUS-SNAP in the KGlu and KCl buffer is 57°C and 53°C, respectively.We also tested the SNAPtag alone as a control.The apparent unfolding temperature of SNAP in the KGlu and KCl buffer is 65°C and 69°C, respectively (Supplementary Fig. S6).Surprisingly, in the KGlu buffer, SNAP has lower apparent unfolding temperature than in the KCl buffer.Therefore, the enhanced thermal stability of FUS-SNAP in glutamate can be attributed to FUS and not to SNAP.Taken together, the FCS and nanoDSF measurements demonstrate that glutamate enhances intramolecular and intermolecular interactions among FUS molecules when compared to KCl.S4).Additionally, the free dye measurement of Rhodamine (Rh110) is given as reference (grey) in panel c.The correlation curve for the cluster cut displays in KGlu (dark blue) a clear shift to longer diffusion times in the oligomer time window when compared to KCl (red).The monomer component (dashed black) is adequately fitted with one diffusion time for both buffers (see Supplementary Table S3).(e) The maximum entropy method (MEM) gives diffusion time distributions (101 components) as a function of probability with one peak between 0.09 and 0.4 ms (monomer time window, green) and a second peal between 0.8 and 4 ms (oligomer time window, pink).(f) Corresponding L-curves according to Vinogradov et al., 62 are presented as quality validation for the obtained diffusion time distributions where the corner point is indicated by a circle.(panels g-h).NanoDSF data show the ratio of 350 nm/330 nm plotted against temperature for FUS SNAP in KCl and KGlu buffers.(h) The first derivative of data shown in (g) against temperature shows the apparent unfolding temperature of FUS-SNAP at 57°C and 53°C in KGlu and KCl buffers, respectively.
Comment 3: Importantly, in the absence of a precise estimation of the size of the clusters in terms of mass or number of proteins, any thermodynamic arguments or estimates related to the free energy of transfer of FUS molecules from the dispersed phase into mesoscale clusters in glutamate versus chloride cannot be made.For example, on L172-173, the authors estimate that this difference is 0.5-0.75kcal/mol, but this must come from a tacit assumption that the abundance of mesoscale clusters is a direct measure of the amount of protein molecules contained in them, which need not be the case.As already mentioned, the authors should measure the sizes of clusters in terms of the mass of proteins they contain or, at least, clearly state and critically discuss the assumptions behind connecting cluster sizes with protein mass.In general, the authors should from the start precisely define what they mean by "size of clusters" throughout.This is not just a semantic point, but rather concerns the very essence of the arguments made.
Response to comment 3: By cluster size, we refer to the number of molecules per cluster.This point has been spelled out very clearly.This is perfectly valid, since there is no evidence that there are drastic conformational changes across the two buffers, and the fluorescence data are unambiguous in terms of the origins of clustering between intermolecular associations as opposed to intramolecular conformational changes.However, the cluster distributions are heterogeneous, and we do not have precise values for P(n) as a function of n.We have used the maximum entropy method to estimate this distribution, but it is an estimate.Therefore, we have deleted any mentions of transfer free energies.Response to comment 4: The formalism of Kirkwood and Buff is the most rigorous description of solution thermodynamics in ternary mixtures and of preferential interactions, which are quantified by the coefficients that we calculate from simulations.In accord with the parsing of Record and coworkers, we conclude that the associations of FET proteins appear to be driven by the preferential exclusion of glutamate when compared to chloride.However, our site-specific radial distribution functions, detailed in Supplementary Figs.S9 -S12, show that there are discrepancies between inferences drawn by Record and co-workers and our computations for sp 2 and cationic nitrogen atoms.
We have added a detailed discussion of this issue.Please see the revised discussion section, especially the section that starts on line 550, which we reproduce below.
We used molecular simulations to quantify preferential interaction coefficients for KCl and KGlu around amino acids with different sidechain chemistries.In line with the proposals of Record and coworkers 44, 45, 53, 54 , our simulations show that glutamate is preferentially excluded from backbone and sidechain amides, as well as other functional groups.However, there are key differences in the atomic-level details that emerge from our simulations versus interpretations proposed by Record and colleagues 44,45,53,54 .Cheng et al., used vapor pressure osmometry (VPO) to measure the solubilities of model compounds in aqueous solvents with different types of solutes 44 .In their notation, water, the primary component is labeled 1, the model compound of interest is component 2, and the solute of interest, such as KGlu or KCl, is compound 3.The change in solubility, as gleaned from VPO measurements, leads to inferences regarding the sign and magnitude of the chemical potential µ23 for the preferential interaction of the model compound with the solute.A positive sign indicates preferential exclusion, whereas a negative sign implies preferential interactions.The measured µ23 values for fifteen different model compounds were decomposed using a global regression analysis based on a linear superposition model 44 .This model is written as: µ23 = ∑aiAi.Here, the summation is over atoms of functional groups in the model compounds and Ai is the solvent accessible surface area of atom i within the model compounds.The values of Ai are computed using a specific probe radius using structures for each model compound.Cheng et al. derived values of ai from a global regression analysis of µ23 values for fifteen model compounds.Based on the inferred values of ai, interactions of glutamate are proposed to be favorable for sp 2 nitrogen atoms and the nitrogen atoms of cationic residues.The converse was found to be true for chloride.Radial distribution functions from our simulations suggest the opposite trends when compared to the inferences of Cheng et al. (Supplementary Figs.S9-S12).For sp 2 oxygen and backbone carbon atoms, Cheng et al., 44 inferred weaker interactions with chloride when compared to glutamate.Our simulation results show similar trends (Supplementary Figs.S9-S12).
What might be the source of discrepancies between inferences from analysis of VPO measurements versus results from simulations for sp 2 nitrogen atoms and the nitrogen atoms of cationic residues?Unlike the analysis of Cheng et al., 44 the inferences from simulations were derived via a detailed accounting of the interplay of amino-acid, water, and solute interactions.The experimental data report one number for each model compound, and these are then dissected using an accessible surface area-based model combined with global regression analysis.There has been considerable debate regarding the use of solvent accessible areas for parsing measurements and drawing inferences regarding solvation thermodynamics 79, 80 .The gist is that the use of accessible surface area as a measure of solvation is problematic for small molecules and atomic-level dissections.Accessible surface area only becomes a useful proxy only at larger length scales 80, 81 .This is because the concept of an interfacial tension does not apply on the atomic and molecular length scales.Instead, theory and simulation suggest that the hydration thermodynamics and forces require the inclusion of a volume term and dispersion interactions on atomic and molecular scales 82 .These are fully present in our simulations.Additionally, solvent accessible surface area is insensitive to changes in conformation and the local concentrations of functional groups for linear, flexible systems 83 .Hence, while the use of solvent accessible surface area is widely prevalent in the protein folding literature, and has been justified by elegant connections to the rigorous Kirkwood-Buff integrals 84 , their use for dissecting atomic-level interactions of disordered proteins remains questionable.The preferential interaction coefficients we compute are directly gleaned from pair distribution functions, in accord with the Kirkwood-Buff formalism 85 .At this juncture, we lean on consistencies of interpretations from the work of Cheng et al., 44 and the simulations.Both sets of studies suggest that the central differences between chloride and glutamate derive from the latter being preferentially excluded from protein sites.
Comment 5: What is the contribution of protein net charge to the observed effects?E.g. Figure 2. g-i the net charges of the constructs are 10, -1, 12, respectively.As Glu is both a pi system and an anion, are there any implications concerning the anion-pi interactions?
Response to comment 5: We draw the reviewer's attention to data for the variant of FUS where we replace 10 Asp residues and 4 Glu residues to Gly (10D/4E-G).If there are anion-π interactions, then they have a destabilizing effect, because as noted in the text, clusters with this variant are readily detectable in the nanomolar concentration regime, whereas mutations of the aromatic residues within the RBD of FUS require concentrations of 10 µM for clusters to be observed.Comment 6: On p. 4, the authors claim that "In KGlu, the slow modes appear at protein concentrations of 2 μM (Supplementary Figure 2e), whereas in KCl they appear at 3 μM.These results provide independent confirmation of the estimates of csat and emphasize the small differences in driving forces for macrophase separation of FUS-SNAP in 100 mM KCl versus 100 mm KGlu".How significant is this difference?Also, there does not appear to be a strong difference between panels in Supplementary Figures 2a and g.Moreover, since the sample is polydisperse, were there any regularization fits used to obtain size distributions?Also, the effect on the autocorrelation curves looks more prominent in panel c and not so in f.Since DLS has a detection limit, (e.g.0.5 mg/ml or so), autocorrelation curves should also presented for low protein concentrations (below 1 µM).

Response to comment 6:
We provide the numbers for csat measured using the Bradford assay and inferred using the DLS data.They are consistent with one another.With the Bradford assay, we estimate csat values of 2 µM in KGlu and 3 µM in KCl.The autocorrelation curves show that slow modes appear at 2 µM in KGlu and at 3 µM in KCl.Two independent methods yield consistent inferences.The revised supplementary materials include data for lower concentrations as requested by the reviewer.Please see Supplementary Fig. S2, which we reproduce below.gamut of species that contribute to the cluster size distributions -defined as the number of molecules per cluster.

Comment 8:
The claimed difference between Arg and Lys residues should be more precisely phrased and better explained in light of the existing literature on the topic (p. 8 "Indeed, it is noteworthy that the free energies of solvation of Arg and Lys are fundamentally different from one another.From this hydration perspective, Arg has more of a hydrophobic character than Lys.As a result, the driving forces for phase separation, which are governed mainly by solubility, are affected by the substitution of Arg to Lys significantly.")Response to comment 8: We urge the reviewer to read the sentences in question in the context of the paragraph in which they are incorporated.Here is the relevant paragraph, which starts on line 381.We have asked colleagues to read this for us, and we do not understand what is imprecise about our verbiage.Arg is more hydrophobic than Lys, and this point has been made most unambiguously by the analysis published by Fossat et al., which we cite in our manuscript.
Substituting 24 Arg residues in the RBD to Lys increases csat by an order of magnitude compared to wildtype FUS 15 .Strikingly, while these substitutions weaken clustering in the presence of 100 mM KCl (Fig. 5c), the extent of clustering we observe in the presence of 100 mM KGlu is similar to that of wild-type FUS (compare Fig. 5c to Supplementary Fig. S5g).As shown in recent single-molecule studies, there is a uniform weakening of cation-π interactions in chloride salts 71 .In contrast, in glutamate, the differences between wild-type FUS and the 24R-K variant seem to be length-scale dependent.Specifically, while clustering, which is mainly impacted by cation-π interactions, is preserved upon substituting Arg to Lys, phase separation, which should be governed mainly by solubility, is weakened by Arg to Ly substitutions.This can be rationalized if the strengths of cation-π interactions are minimally affected by glutamate compared to chloride.However, the increase in csat points to differences in solubility driven by substitutions of Arg to Lys.Indeed, it is noteworthy that the free energies of solvation of Arg and Lys are fundamentally different from one another 72 , and Arg has more of a hydrophobic character than Lys 72 .As a result, the driving forces for phase separation, which are governed by solubility limits, are affected by substitutions of Arg to Lys, whereas clustering in sub-saturated solutions is not affected, especially in glutamate.
Comment 9: On p. 6, the authors claim that "Further, measurements of fluorescence correlation spectroscopy (FCS) on the single-molecule level show that the autocorrelation of donor-labelled FUS-SNAP is consistent with increased translational diffusion time td2 and strong fluctuation in the weighted residuals at correlation times longer than td2 in the KGlu buffer (Supplementary Figure 3f).This points to the presence of higher-order complexes even at 400 pM concentrations of FUS-SNAP.".However, it is hard to see any difference.This should be shown quantitatively together with an estimation of how significant the effect is.Also, since here one again deals with polydisperse media, how appropriate is it to just use a two-component fit?
Response comment 9: We direct the reviewer's attention to the new Fig. 4 and the new Supplementary Fig. S6.Please also see the detailed response to comment 2.
Comment 10: Some ring-containing amino acids (at least Tyr) should be added to the list of those studied by MD simulations, especially considering their importance in condensate formation.Moreover, some RDFs (SI Fig. 5.) from MD simulations do not seem to fully converge at the studied distances (e.g.Lys or Arg).This should be extended.
Response to comment 10: The requested additions and extensions have been made.Please see the revised Fig. 8 and the new Supplementary Figs.S9-S12.

Size distributions of low abundance mesoscale clusters from analysis of DLS data:
The mesoscale clusters represent 0.1% -1% of all species that are present in sub-saturated solutions.The abundance of mesoscale clusters is higher in glutamate than in chloride, especially well below csat (Fig. 3a-3c).We used the number density of scatterers, extracted from the DLS data, and quantified the distribution of hydrodynamic diameters (dH) of mesoscale clusters.We used this analysis to ask and answer the following questions: On the manifold of mesoscale species that are the least abundant, albeit largest species that form in sub-saturated solutions, what is the frequency of observing specific dH values?If we use this distribution to estimate the molecularity distributions, which refer to the frequency or probability of observing mesoscale clusters with n molecules, what types of distributions do we obtain?Specifically, is there evidence for continuous evolution of the heavy tail in the cluster size distribution as depicted in Fig. 1, and is this evolution different in KCl versus KGlu?To answer these questions, we leveraged the fact that information regarding the time correlation functions combined with information regarding raw intensities can be used to extract distributions of scattering intensities, which scale as the sixth power of the hydrodynamic diameter dH.Using the Stokes-Einstein formula, these intensity distributions can be used to estimate the number densities of dH values.Following the approach of Cohan et al., 68 the intensity distributions were converted to distributions of dH values using practical implementations of Mie scattering theory 66 .We extracted distributions of dH values for FUS-SNAP at different protein concentrations.All measurements were performed in sub-saturated solutions.We compared the distributions in 100 mM KCl versus 100 mM KGlu (Fig. 4a-4d) at different protein concentrations.For three of the four protein concentrations (0.125 µM, 0.25 µM, and 0.5 µM) the size distributions in KGlu are shifted to higher values when compared to KCl.The distributions in KGlu and KCl show the heavy tail nature that we anticipate from theory (Fig. 1).This point becomes clear when one accounts for the abundance of the mesoscale clusters, which we measured using NTA.
Interestingly, the continuous growth of mesoscale species with increased protein concentrations plateaus in KGlu as csat is approached.As a result, in a 1 µM protein solution, the distribution of dH values in KCl catch up with the distributions in KGlu.This observation helps explain the similarities of csat values that we estimated in KCl and KGlu.It is also in line with the theories 46,50 , where the entropy of mixing becomes considerably less favorable as molecular or cluster sizes decrease -a phenomenon referred to as an entropic sink by Bracha et al., 69 .
Next, we converted the distribution of dH values to estimate the molecularity distributions, i.e., the distribution of number of molecules within a mesoscale cluster.To extract these distributions, we use the fact that the dH of monomeric FUS-SNAP is 4.6 nm (see below for a direct measurement).Assuming a spherical approximation for the monomers, the number of molecules n within a cluster of hydrodynamic diameter dH can be estimated as: n = p(vc/vm).Here, vc and vm are the volumes of the cluster and monomer, respectively and p is a dimensionless packing fraction.The upper limit on p is 0.74 for crystalline packing of monomers within a cluster.If we assume random close packing of spheres, then p = 0.64.Conversely, if we assume that molecules are packed within clusters as they would be in dense phases, where the volume fraction of solvent is between 0.6 and 0.7, then we can set p = 0.33 25,26,27,32,70 .
We analyzed the molecularity distributions for mesoscale clusters formed by FUS-SNAP by assuming two different values for p viz., 0.64 (Fig. 4d-4g) and 0.33 (Fig. 4h -4k).Both assumptions paint a similar picture.The low abundance mesoscale clusters, which should be in the tails of the cluster size distribution, show a rightward shift toward larger numbers with increasing protein concentration.The cluster sizes in KGlu are larger than in KCl for three of the four concentrations.As csat is approached, the cluster sizes stop growing in KGlu, and the cluster size distribution in KCl becomes akin to what is observed in KGlu.When comparing these cluster size distributions to what we anticipate from theory (Fig. 1), it is important to remember that we are analyzing cluster sizes on the manifold of mesoscale species, whose abundance is low, in the range of 0.1% -1%.

Summary comment:
We understand that the introduction of new ideas is difficult to accept.With all due respect, we submit that the case we have presented for pre-percolation clusters, their adherence to the tenets of the physics of associative polymers, and the range of experiments and analyses we have brought to bear far exceeds anything that has been produced in the phase separation or condensate literature.We hope that the reviewer will see reason and grant that we have provided more than definitive evidence for our case.

Fig. 7 :
Fig. 7: FUS-SNAP clusters create distinct local environments.(a) The fluorescence lifetimes of Nile Red with various concentrations of FUS-SNAP equilibrated for 30 minutes in KGlu and KCl buffer.(b)-(d) The different concentrations of FUS-SNAP solutions and buffers are mixed with 2 µM bis-ANS in 100 mM KGlu buffer (b), 100 mM KCl buffer (c), and 200 mM KCl buffer (d).For bis-ANS studies (b)-(d), the mixture solutions were excited using a 355 nm laser, and the emission spectra were measured from 425 nm to 650 nm.

Fig. 4 :
Fig. 4: Compared to KCl, KGlu stabilizes FUS-SNAP clusters even at ultra-low concentrations.(a) IUPRED predictions of disorder of FUS-SNAP.(b) Single-molecule detection (SMD) fluorescence intensity traces of 200 pM FUS-SNAP-AF488 in both buffers with indicated threshold for cluster cut (yellow-green) and monomer reference cut (pink).These traces display the pronounced clustering behavior in KGlu compared to KCl. (c-d) Autocorrelation curves for FUS-SNAP-AF488 with blow-ups for the monomer time window (yellow-green) and oligomer time window (pink) show the resulting translational diffusion times (dashed lines) including one global and buffer-dependent time for a 3D-Gaussian diffusion model and the weighted residuals for the cluster cut and the monomer cut as reference.The fit to eq. 6a (see Methods) in panel c yields identical diffusion times within error in KCl ( !,#$ (&'() = 0.189 ± 0.017 ms, orange) and KGlu ( !,#$ (&'() = 0.201 ± 0.017 ms, blue (for all fit results see

Comment 4 :
Record and coworkers (PMID: 27806267, 27054379) have provided a quantitative model of how Glu impacts protein stability in relation to the amount and composition of surface area exposed or buried.While the authors cite these studies, they contain much more relevant information than presently exploited by the authors.In particular, the authors should study the predictions of the model by Record et al. in the case of FUS sequence and critically analyze what they imply about their findings.

Fig. 4 :
Fig. 4: Size and molecularity distributions of low abundance, mesoscale clusters.We extracted the distributions of dH values for FUS-SNAP at different protein concentrations, all of which were in the sub-saturated regime.The top row panels (a) -(d) show the distribution of dH values extracted in KGlu (dotted curves) and KCl (solid curves) for solutions with protein concentrations of 0.125 µM (a), 0.25 µM (b), 0.5 µM (c), and 1 µM (d).These distributions are shown as raw histograms, and hence the ordinate shows frequencies i.e., the number of occurrences of a dH value between dH and dH + ∆, where ∆ = 0.1 nm.In each panel, the abundance of species being analyzed is shown in the legend, and these values were extracted from NTA data shown in Fig. 3b.Rows 2 and 3 show the molecularity distributions, where molecularity refers to the number of molecules n within a cluster of size dH.These distributions were computed by assuming that the molecules within clusters are spheres.The packing fraction can be set to be p = 0.64, for random close packing of spheres, panels (e)-(g) or p = 0.33, panels (h) -(k), assuming a packing density concordant with reports of the volume fractions of protein versus solvent in single protein condensates 25, 26, 27 .In each panel, the solid curve corresponds to KCl, and the dotted curve corresponds to KGlu.The concentration of [FUS-SNAP] for each column of plots is shown at the top.